Proof. We have seen here that:
\begin{align*}
\sin^2(x) + \cos^2(x) = 1.
\end{align*}\begin{align*}
\frac{\sin^2(x)}{\cos^2(x)} + 1 = \frac{1}{\cos^2(x)}.
\end{align*}\begin{align*}
\tan^2(x) + 1 = \sec^2(x).
\end{align*}
tan^2(x) + 1 = sec^2(x)
Prove that tan^2(x) + 1 = sec^2(x)
The function \tan^2(x) + 1 is equal to \sec^2(x).
Proof. We have seen here that:
Now multiply both sides with \frac{1}{\cos^2(x)} gives us:
We do know that \frac{\sin^2(x)}{\cos^2(x)} = \tan^2(x) and \frac{1}{\cos^2(x)} = \sec^2(x). Therefore, we get the following:
Therefore, \tan^2(x) + 1 is equal to \sec^2(x).
Proof. We have seen here that: